As someone who works in a jewelry store and does sizing on many occasions, this kind of piece is something that most jewelers would not try to size. Any time you size a ring you almost always need to bring heat into the equation. And Lapis is not a great choice for long term durable ring wear, and I do not think it can take the kind of heat that sizing requires. For engagement stones you really want a 9 or 10 on the scale which includes Sapphires, Rubies, Diamonds and a few other "man made" gemstones. Anything lower may get damaged and will not look as sparkly over time (trust me I've seen a morganite ring after a week).
I agree that the seller is handling the customer service part terribly, but this design just does not have the long term wearability required of an engagement ring. They should have never advertised it as an engagement ring, but being in the business you would not believe the rings I've seen come in as "Engagement Rings".
Wherever you choose your next ring please remember that a ring is a like a car, it needs to be serviced every now and again. You need to have it cleaned, checked and possibly repaired. Etsy is great for short term, but who will size your ring if you have a baby someday? How will you get it fixed if it breaks? Even if a jewelry store may be daunting, its one of the only industries where they are required to service the ring for its lifetime, so definitely take advantage of it
If you have ANY questions about metals, rings, sizing, stone hardness, Anything related to engagement ring shopping please send me a Pm! There is just so much that goes into it that you can really only get from an inperson jewelr.
Also in the future when you get sized be sure they are sizing you with a smaller band sizer vs something thick. The thinner the band the smaller it needs to be and vice versa. So a thick size 6 and a thin size 6 will fit very differently on your finger.
*Or if you need a good custom engagement ring let me know